How many children attended the auto show

Question

to attend a local auto show, children admission was $7, adult admission was $11, and senior admission was $9. In all, 224 people attended the show, bringing in a total of $2116 of admission sales. Prior to leaving, every adult and senior filled out one free raffle ticket for a chance to win a new mustang. A total of 176 raffle tickets were filled out. How many children attended the auto show? How many adults attended the auto show? How many seniors attended the auto show? 

Answer 1

This type of but it takes a lot of time and different steps but you can do it.

  

let

 

C be the number of children

A be the number of adults

S be the number of seniors

 

Write down everything you were given in the problem

 

 

C ($7) + A ( $11) + S ($9) = $2116   You know how much was paid given the price per ticket.

C + A + S                          = 224       You know the total number of people who attended the show

A+S                                   =176      You know the number of Adults and Seniors 

 

 

So, know you need to solve for C,A,S.

 

If A+S =176, then you can substitute that in the second equation above and rewrite it as:

 

C + (176)= 224

 

So, C = 48

then substitute 48 for C in the first equation

 

48 ($7) + A ( $11) + S ($9) = $2116

$336  + A ($11) + S ( $9)    = $2116  

 

now subtract $336 from both sides

 

A ($11) + S($9)  = $1780

remember that you know that A + S = 176   ( see above)

 

So you know have two equations with two unknowns.

 

A ($11) + S($9) = $1780

A + S                =176

 

now you use substitution

 

subtract S from both sides and you get

 

A= 176-S

 

You that to solve

A ($11) + S($9) = $1780

 ( 176-S) ($11) + S($9) =$1780

 

use the distributive property to multiply

 

$1936-S($11) +S($9) =$1780  

 

1936-S(11) +S(9)=1780    ( I dropped the dollar signs for now)

 

you know want to solve for S

 

combine the Ss and move them to one side of the equation

 

1936-2S=1780

 

1936-1780= 2S

156           =2S

 

78             =S

 

and since you know that S + A = 176

then A = 98

 

So, there you have it.

 

C=48

A=98

S=78

 

 

 

 

 

 

Answer 2

Hi Kayla,

Use variables to represent the unknowns using given information.

 

Let:

x = no. of adults

176-x = no. of seniors

224-176 = 48  no. of children

 

We have figured out the number of children, we just have to figure out the number of adults and seniors. Although this problem has 2 more unknowns, we can just use 1 equation to solve 

 

kids ticket sales + adults ticket sales + seniors ticket sales = total sales

 

7(48) + 11x + 9(176-x) = 2116

 

336 + 11x + 1584 - 9x = 2116

1920 + 2x = 2116

-1920         -1920

--------        -------

         2x = 196

         ---    ----

          2      2

          x = 98

 

x = 98 = no. of afult tickets sold

176-98 = 78 = no. of senior tickets sold

224 - 176 =  48 = no. of children tickets sold

 

you can check your answer by plugging in these values and calculate the total sales, it should equal $2,116

 

Hope it helps.

 

 

 

Answer 3

Hi Kayla,

Suppose no of children attended auto show = x

             no of adult attended auto show= y

             noof senior attended auto show = z

Total = 224

so x+y+z=224.......... eq 1

 

7x+11y+9z= 2116.....eq 2

 

y+ z = 176.........eq 3,

 

subtracting eq 3 from eq 1, we get

x= 224-176 = 48

substituting value of x in eq 2, we get 7(48) +11y+9z=2116, 

                                                                  11y +9z =1780  ..... eq 4

now multiply eq 3 by 11,                               11y +11z =1936 .... eq 5

subtracting eq 4  from eq 5, we get 2z= 156

                                                     z= 78

y+z= 176

y+78=176

  y=98

 # of kids= 48, # of adults=98, # of seniors= 78

Check your answer.